Spectral Representation of EEG Data using Learned Graphs with Application to Motor Imagery Decoding

Abstract

Objective: This paper presents a graph signal processing (GSP)-based approach for decoding two-class motor imagery EEG data via deriving task-specific discriminative features. Methods: First, a graph learning (GL) method is used to learn subject-specific graphs from EEG signals. Second, by diagonalizing the normalized Laplacian matrix of each subject graph, an orthonormal basis is obtained using which the graph Fourier transform (GFT) of the EEG signals is computed. Third, the GFT coefficients are mapped into a discriminative subspace for differentiating two class data using a projection matrix obtained by the Fukunaga-Koontz transform (FKT). Finally, an SVM classifier is trained and tested on the variance of the resulting features to differentiate motor imagery classes. Results: The proposed method is evaluated on Dataset IVa of the BCI Competition III and its performance is compared to i) using features extracted on a graph constructed by Pearson correlation coefficients and ii) three state-of-the-art alternative methods. Conclusion: Experimental results indicate the superiority of the proposed method over alternative methods, reflecting the added benefit of integrating elements from GL, GSP and FKT. Significance: The proposed method and results underpin the importance of integrating spatial and temporal characteristics of EEG signals in extracting features that can more powerfully differentiate motor imagery classes.

Voxel-Wise Brain Graphs from Diffusion MRI: Intrinsic Eigenspace Dimensionality and Application to Functional MRI

“…That is, functional patterns are smooth relative to the underlying fiber architecture and tissue profile morphologies. This observation is, on the one hand, consistent with the energy profile of fMRI graph signals on voxel-wise gray matter graphs (Behjat et al, 2015, as well as region-wise brain graphs (Atasoy et al, 2017;Preti and Van De Ville, 2019;Glomb et al, 2020;Miri et al, 2022), which is reminiscent of a power-law behavior, and on the other hand, can be linked to the decreasing trend observed in the Procrustes validation errors (see Fig. 3(D)), where increasing K-values reduce the error close to that of a randomly generated graph.…”

“…GSP has found numerous applications across multiple domains—see e.g. (Ortega et al, 2018) for a recent review, and in particular within neuroimaging, examples include: brain state decoding (Petrantonakis and Kompatsiaris, 2018; Ghoroghchian et al, 2020; Georgiadis et al, 2021; Cattai et al, 2021; Miri et al, 2022), brain signal denoising (Einizade and Sardouie, 2022), brain activation mapping (Behjat et al, 2015; Abramian et al, 2021) and source localization (Hyde et al, 2019), diagnosing neuropathology (Itani and Thanou, 2021; Jafadideh and Asl, 2022), tracking fast spatiotemporal cortical dynamics (Glomb et al, 2020; Rué-Queralt et al, 2021), brain fingerprinting and task decoding (Griffa et al, 2022), identifying dynamically evolving populations of neurons (Charles et al, 2022), deciphering signatures of attention switching (Medaglia et al, 2018; Huang et al, 2018), manifesting white matter pathways that mediate cortical activity (Tarun et al, 2020), and elucidating perturbations of consciousness induced by brain injury or drugs (Atasoy et al, 2017; Luppi et al, 2022).…”

Brain fingerprinting using EEG graph inference

“…replacing the ℓ 2 -norm with a logarithmic barrier, the optimization in (2) can be solved more efficiently via a more general-purpose formulation with respect to the graph’s adjacency matrix [11]: where Z is an N × N matrix with elements Z i,j = ∥ F i ,: − F j ,: ∥ 2 , i.e., Euclidean distance between signal values on electrodes i and j . The first term in (3) enforces the smoothness constraint in similar way as in the first term in (2), which is based on the equivalence trace( F T LF ) = 0.5 ∥ A ◦ Z ∥ 1 , where ◦ is the Hadamard product [19]. Intuitively, if smooth graph signals reside on well-connected vertices, it is expected that these vertices have smaller distances Z i,j .…”

“…where • is the Hadamard product [19]. Intuitively, if smooth graph signals reside on well-connected vertices, it is expected that these vertices have smaller distances Z i,j .…”

“…A closely related method has already shown promising results on fMRI data [8]. Here we focus on EEG data, leveraging our recently proposed method for inferring brain graphs from EEG data [19]. This method results in a graph that captures subtle spatial relations between EEG electrodes, in particular, their instantaneous spatial profiles, such that EEG maps can be seen as smooth functions on the resulting graphs.…”